Knowledge of the vertical liquid flux rate in vadose zones is required for recharge investigations to evaluate contaminant travel times and estimate transport loading to underlying aquifers. The Darcian approach is commonly used as a first order analysis to estimate liquid flux in the vadose zone (Gee and Hillel, 1988; Allison et al., 1994; Stephens, 1996). In this approach, flux is estimated as the product of vertical hydraulic gradient and unsaturated hydraulic conductivity over a range of measured water potentials or water content. In the case where water potential is the same throughout the profile indicating uniform steady state drainage, then a unit hydraulic gradient exists and the unsaturated hydraulic conductivity is equivalent to the vertical flux (Black, et al., 1969; Sisson and van Genuchten, 1980). Water potential is the potential energy of water relative to pure free water including matrix, gravimetric, pressure, humidity and solute effects. In this discussion, the gravimetric and matric effects are considered the dominant forces.
Estimates of hydraulic conductivity can be developed from steady state techniques presented by Klute and Dirksen (1986). These methods rely on application of equal water potential or constant flux across a vertical core sample to produce a unit gradient, and measurement of the volume of water that enters and exits the sample per unit time. Porous plates used in these procedures may impede flow so the hydraulic gradients are confirmed using tensiometers in the sample. For the constant head test, the upper and lower heads are controlled by hanging water columns with water added using a Mariotte chamber apparatus. The short column version works with undisturbed or repacked, fine grained materials and requires less time to reach steady state conditions with thin samples (Klute and Dirksen, 1986). The volume or mass of water that drains from the bottom of the core is measured to estimate the flux at the measured water potential. The accuracy and range of measurements are controlled by the precision of the water measurement technique used in the test. The long column technique works with disturbed (repacked) samples, is generally limited to higher water contents, relatively coarse materials and requires extended time periods to establish steady state flow conditions (Klute and Dirksen, 1986).
The technique proposed herein is related to field approaches such as the crust method suggested by Hillel and Gardner (1970) and developed for field use by Bouma et al. (1971) where the water flux is maintained at a value below the saturated conductivity under steady flow. It is also similar to the sprinkler imposed steady state flux method (field) proposed by Youngs (1964).
The Darcian approach used to estimate flux is typically applied at shallow depths where water potentials fluctuate over a wide range in days to months, causing large changes in hydraulic gradients and hydraulic conductivity (Stephens and Knolton, 1986). The shallow oscillatory fluctuations also induce hysteresis, introducing additional error into the hydraulic conductivity estimates due to the non-linear relationship of the soil moisture characteristic curve. Large variations in water potential at these depths may necessitate the use of an instrument or a combination of instruments that sense over a wide range, but are less precise than direct measurement sensors (for example, a tensiometer). Measurements from near surface instruments are also often influenced by large temperature fluctuations. These temperature fluctuations influence the sensor's electronic output or the expansion and contraction of contained water in a tensiometer (Hubbell and Sisson, 1998). Conventional tensiometers located at shallow depths require greater field maintenance than instruments at deeper depths and may introduce systematic errors from diurnal and seasonal temperature variations. These problems are reduced by the use of advanced tensiometers which require less maintenance than standard tensiometers and are less affected by temperature fluctuations due to placement of the sensor near the point of measurement (Hubbell and Sisson, 1998).
Water potential measurements in sediments taken at greater depths typically will indicate a unit hydraulic gradient under steady state drainage conditions (Black et al., 1969). McElroy and Hubbell (2004) found that water potential measurements in a deep vadose zone (from 7- to 73-m depths) showed a near unit vertical hydraulic gradient and commonly exhibited near steady state water potentials. They also reported that tensiometer measurements in deep sedimentary interbeds at 34- to 73-m depths at a ponded infiltration site with high flows (over 340 m3 day−1) had hydraulic gradients from 0.94 to 1.04 during the ponding. This information supports the assumption of a near unit gradient under both ambient and induced recharge events. These water potential measurements in the deep vadose zones were all within the tensiometric range (Hubbell et al., 2002) and were either stable or gradually trending towards a stable condition suggestive that it is appropriate to assume steady-state vertical flow. From Richards' equation for vertical flow, steady state behavior can only occur when water potential gradients are negligible (uniform water potential with depth), and flow is driven solely by the gravitational component of the hydraulic gradient, which is unity.
Dirksen (1979) indicated that the most accurate water flux estimates are obtained under steady state conditions where the water contents do not change with time so that the water fluxes are equal to the externally measured inflow and outflow. Then the soil hydraulic conductivity curve (Ku) function can be determined by a series of steady state measurements. Montazer (1986), Gee and Hillel (1988), Scanlon et al. (1997) and Hubbell et al. (2004) noted that deep vadose zones in arid and semiarid environments typically exhibit minor and slow changes in water potentials over time.
Hubbell et al. (2004) concluded that the high degree of uncertainty associated with the mapping of water potential to the unsaturated hydraulic conductivity makes it difficult to estimate the distribution of flux in the deep vadose zone. They suggested that Darcian flux estimates could be improved if the unsaturated hydraulic conductivity estimates were more representative.
Two techniques, the steady state laboratory methods (Klute and Dirkson, 1986) and the ultracentrifuge method (Conca and Wright, 1990) are preferred over the transient methods such as the instantaneous profile (Watson, 1966), pressure-plate (Gardner, 1955), one-step outflow (Doering, 1965), and the methods by Ahuja and El-Swaify (1976) modified and discussed by Butters and Duchateau (2002). Steady state tests have advantages over multiple step tests in that they: 1) require just one constant pressure step to be performed, 2) reduce errors imparted by water potential changes within the sample, 3) reduce estimation errors from transient measurements, 4) ensure a unit gradient over the sample by the test design, and 5) produce resultant data that reflect the actual hydraulic conditions of the in situ sample. Performing the test at only one water potential/pressure also reduces the time to conduct this laboratory procedure.
The unsaturated hydraulic conductivity at a designated water potential also depends on whether the sample is wetting or drying. The hydraulic conductivity values on the drying curve are lower than on the wetting portion of the curve, and varies more from the wetting curve in coarser textured materials (Stephens, 1996).
Many investigations desire to estimate the liquid fluxes over a wide range of values that may be anticipated in the vadose zone. Scanlon et al. (1997) compiled water fluxes ranging from near zero to 60 cm yr−1 in arid zone experiments using various estimation techniques. However, the typical range of fluxes anticipated for semi-arid sites are in the range of 0.1 to 10 cm yr−1. This range corresponds to hydraulic conductivities from 3.2E-9 to 3.2E-7 cm sec−1, assuming vertical flow and a unit hydraulic gradient.
The laboratory measured saturated hydraulic conductivity (Ks) is commonly employed for estimating the unsaturated hydraulic conductivity curve, but its use can have disadvantages. The saturated hydraulic conductivity test may have measurement errors from fluid channeling along the sidewall of the core, producing unrepresentative high values. This would bias the values plotted in the entire unsaturated hydraulic conductivity curve (Ku) because the saturated hydraulic conductivity is the upper end point of the Ku curve.
One embodiment of the invention is a steady state measurement technique (and apparatus) for unsaturated hydraulic conductivity at a specified water potential [K(ψ)] at a specified water potential (ψ) representative of field conditions. The measured K(ψ) can be used to develop the Ku curve by using the K(ψ) as a reference point instead of the Ks which may vary orders of magnitude from the field unsaturated hydraulic conductivity.